Continuous Correction Functions for Dynamic Route Choice Algorithms

Dynamic traffic assignment algorithms typically proceed by iterating between route swapping and dynamic network loading. This chapter considers various route swap processes and investigated their convergence to equilibrium (assuming that the route cost vector is a monotone function of the route flow vector). Pairwise swapping (in which swapping can occur between each pair of routes) is shown to converge even with an arbitrary exponent on the cost differences (in the dynamic model and hence also in the steady state model). When swapping is only to the least costly route (for that origin destination (OD) pair), convergence is shown in the steady state model. Various forms of convergence measure were considered; this form is suggested by the route swap process. Equivalences were established between the different forms in that if one converged to zero (for a particular route swap process) then so would the other. These equivalences are independent of whether the swap process is continuous or discrete (i.e. the integral can be replaced with a sum).